Convexity of yield surface with directional distortional hardening rules

Jiri Plesek, Heidi P Feigenbaum, Yannis F. Dafalias

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

The present paper examines the convexity of the yield surface in the directional distortional hardening models by Feigenbaum and Dafalias. In these models anisotropy develops through kinematic and directional distortional hardening, supplemented by the classical isotropic hardening, and the associative flow rule is used. However, the issue of convexity, which naturally arises due to the distortion of the yield surface, was not fully addressed. The present paper derives the necessary and sufficient conditions to ensure convexity of the yield surface for the simpler Feigenbaum and Dafalias models, but it is not as straightforward to derive corresponding conditions for convexity of the Feigenbaum and Dafalias model version which contains an evolving fourth-order tensor. In this case convexity will be addressed first in general and then at the limit state for which simple restrictions on the material constants to ensure convexity are derived. Numerical examples will show that some of the yield surfaces simulated in the original Feigenbaum and Dafalias publication will not stay convex if loaded beyond what was done in these publications. Therefore the material constants for these cases are recalibrated based on the derived relations for satisfaction of the convexity requirement, and the fitting of the yield surfaces is repeated with the new set of constants and compared with the previous case.

Original languageEnglish (US)
Article number013004QEM
Pages (from-to)477-484
Number of pages8
JournalJournal of Engineering Mechanics
Volume136
Issue number4
DOIs
StatePublished - Apr 2010

Fingerprint

Hardening
Tensors
Kinematics
Anisotropy

Keywords

  • Anisotropy
  • Convexity
  • Elastoplasticity
  • Plasticity
  • Yield surface

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials

Cite this

Convexity of yield surface with directional distortional hardening rules. / Plesek, Jiri; Feigenbaum, Heidi P; Dafalias, Yannis F.

In: Journal of Engineering Mechanics, Vol. 136, No. 4, 013004QEM, 04.2010, p. 477-484.

Research output: Contribution to journalArticle

@article{4315358030b244cbb9216b64a3006bf5,
title = "Convexity of yield surface with directional distortional hardening rules",
abstract = "The present paper examines the convexity of the yield surface in the directional distortional hardening models by Feigenbaum and Dafalias. In these models anisotropy develops through kinematic and directional distortional hardening, supplemented by the classical isotropic hardening, and the associative flow rule is used. However, the issue of convexity, which naturally arises due to the distortion of the yield surface, was not fully addressed. The present paper derives the necessary and sufficient conditions to ensure convexity of the yield surface for the simpler Feigenbaum and Dafalias models, but it is not as straightforward to derive corresponding conditions for convexity of the Feigenbaum and Dafalias model version which contains an evolving fourth-order tensor. In this case convexity will be addressed first in general and then at the limit state for which simple restrictions on the material constants to ensure convexity are derived. Numerical examples will show that some of the yield surfaces simulated in the original Feigenbaum and Dafalias publication will not stay convex if loaded beyond what was done in these publications. Therefore the material constants for these cases are recalibrated based on the derived relations for satisfaction of the convexity requirement, and the fitting of the yield surfaces is repeated with the new set of constants and compared with the previous case.",
keywords = "Anisotropy, Convexity, Elastoplasticity, Plasticity, Yield surface",
author = "Jiri Plesek and Feigenbaum, {Heidi P} and Dafalias, {Yannis F.}",
year = "2010",
month = "4",
doi = "10.1061/(ASCE)EM.1943-7889.0000077",
language = "English (US)",
volume = "136",
pages = "477--484",
journal = "Journal of Engineering Mechanics - ASCE",
issn = "0733-9399",
publisher = "American Society of Civil Engineers (ASCE)",
number = "4",

}

TY - JOUR

T1 - Convexity of yield surface with directional distortional hardening rules

AU - Plesek, Jiri

AU - Feigenbaum, Heidi P

AU - Dafalias, Yannis F.

PY - 2010/4

Y1 - 2010/4

N2 - The present paper examines the convexity of the yield surface in the directional distortional hardening models by Feigenbaum and Dafalias. In these models anisotropy develops through kinematic and directional distortional hardening, supplemented by the classical isotropic hardening, and the associative flow rule is used. However, the issue of convexity, which naturally arises due to the distortion of the yield surface, was not fully addressed. The present paper derives the necessary and sufficient conditions to ensure convexity of the yield surface for the simpler Feigenbaum and Dafalias models, but it is not as straightforward to derive corresponding conditions for convexity of the Feigenbaum and Dafalias model version which contains an evolving fourth-order tensor. In this case convexity will be addressed first in general and then at the limit state for which simple restrictions on the material constants to ensure convexity are derived. Numerical examples will show that some of the yield surfaces simulated in the original Feigenbaum and Dafalias publication will not stay convex if loaded beyond what was done in these publications. Therefore the material constants for these cases are recalibrated based on the derived relations for satisfaction of the convexity requirement, and the fitting of the yield surfaces is repeated with the new set of constants and compared with the previous case.

AB - The present paper examines the convexity of the yield surface in the directional distortional hardening models by Feigenbaum and Dafalias. In these models anisotropy develops through kinematic and directional distortional hardening, supplemented by the classical isotropic hardening, and the associative flow rule is used. However, the issue of convexity, which naturally arises due to the distortion of the yield surface, was not fully addressed. The present paper derives the necessary and sufficient conditions to ensure convexity of the yield surface for the simpler Feigenbaum and Dafalias models, but it is not as straightforward to derive corresponding conditions for convexity of the Feigenbaum and Dafalias model version which contains an evolving fourth-order tensor. In this case convexity will be addressed first in general and then at the limit state for which simple restrictions on the material constants to ensure convexity are derived. Numerical examples will show that some of the yield surfaces simulated in the original Feigenbaum and Dafalias publication will not stay convex if loaded beyond what was done in these publications. Therefore the material constants for these cases are recalibrated based on the derived relations for satisfaction of the convexity requirement, and the fitting of the yield surfaces is repeated with the new set of constants and compared with the previous case.

KW - Anisotropy

KW - Convexity

KW - Elastoplasticity

KW - Plasticity

KW - Yield surface

UR - http://www.scopus.com/inward/record.url?scp=77952269207&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77952269207&partnerID=8YFLogxK

U2 - 10.1061/(ASCE)EM.1943-7889.0000077

DO - 10.1061/(ASCE)EM.1943-7889.0000077

M3 - Article

VL - 136

SP - 477

EP - 484

JO - Journal of Engineering Mechanics - ASCE

JF - Journal of Engineering Mechanics - ASCE

SN - 0733-9399

IS - 4

M1 - 013004QEM

ER -